A car travels from point A to point B. The average speed of

Question

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A. 30
B. 45
C. 60
D. 75
E. 90

A. 30
B. 45
C. 60
D. 75
E. 90

Bunuel · Accepted Answer

A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A. 30
B. 45
C. 60
D. 75
E. 90

A. 30
B. 45
C. 60
D. 75
E. 90

Let the average speed for the second half of the trip be  x  miles per hour.

Pick some smart number for the distance from A to B: let the distance be 180 miles, so half of the distance will be 90 miles.

Average \ speed=\frac{total \ distance}{total \ time}  -->  60=\frac{180}{total \ time} ;

Total time  equals time for the first half  plus  time for the second half -->  \frac{90}{90}+\frac{90}{x}=\frac{x+90}{x} ;

So  60=\frac{180}{total \ time}  -->  60=\frac{180x}{x+90}  -->  60x+60*90=180x  -->  120x=60*90  -->  x=45 .

Answer: B.

PareshGmat · Answer

Let total distance = 2x
Avg Speed = 60

For first half  
Distance = x
Speed = 90

For second Half  
Distance =x
Speed = s (Assume)

Setting up the equation

\frac{x}{90} + \frac{x}{s} = \frac{2x}{60}

s = 45

Answer = B

danzig · Answer

Thanks Bunuel!

An additional question: What is the logic behind picking numbers in this problem? , How do these numbers lead us to the answer?

watwazdaquestion · Answer

180 is the least common multiple of 90 mi/hr and 60 mi/hr. Picking 180 makes calculations easy when you know d = rt

rajathpanta · Answer

how about weighted average for this method? the number between 90 and 60 is 30. So it should be slightly higher than 30 and less than 60. So the ans is 45

GMAT40 · Answer

Let distance be D. Half distance travelled at avg speed of 90m/h. Let x m/h be the avg speed for seconds half of the distance.
Given : Avg speed for the entire trip is 60

D/2/90 + D/2/x = D/60
D/180 + D/2x = D/60
Solving for x, we get 45m/h

Ans: B

jayaddula · Answer

average speed= 2 s1 s2/ s1+s2 (when disctance travelled is equal.)

i

2x 90 x s2
---------- = 60 
90 + s2

180 s2 = 60 (90 + s2)

180s2- 60 s2 = 5400

s2 = 5400 / 120

s2 = 45

jlgdr · Answer

1. Use 180 for each half distance, therefore total distance is 360
2. Total distance / Avg Speed = Total Time---> 360/60 = 60
3. Total time in first leg = 180/90 = 2 hrs
4. Avg speed in second leg= 180/4=45

B

Hope it helps
Cheers
J

singhaldheeraj · Answer

VERY EASY USE THE FORMULA FOR EQUAL DISTANCE TRAVELLED OR HALF DISTANCE

AVERAGE SPEED = 2AB/A+B, WHERE A AND B ARE THE SPEEDS OF THE CAR IN FIRST HALF DISTANCE AND SECOND HALF DISTANCE RESP.

FOR THREE EQUAL DISTANCE USE AVG SPEED = 3ABC/A+B+C ==== SAME AS A,B,C ARE SPPED RESP

IN QUESTION A IS GIVEN FIND OUT B

siggarusfigs · Answer

I am wondering... so "half the trip" refers to distance or to time? If "half the trip" means half of the distance, the answer is 45. If "half the trip" means half of the total time, the answer is 30.

sanket1991 · Answer

Avg. Speed = 2S1S2/(S1+S2),
we know S1 and we know Avg. Speed 
So it is very easy to calculate S2 
Ans. B

vards · Answer

FORMULA FOR CALCULATING AVERAGE SPEED =

Average speed =  \frac{2 * S1 * S2}{S1+ S2}

let speed for 2nd part be X

60 =\frac{2 * 90 * X}{X + 90}

X + 90 = 3X

X = 45

P.S = If 3 speeds - A , B, C are given , then formula is =  \frac{3 * A * B * C}{AB * AC * BC}

Please consider  KUDOS  if my post helped

Ashishmathew01081987 · Answer

I don't think this formula would work always. It worked fine here because both the distances covered were in the ratio 1:1.

Case 1  : If a body travels from Point A to Point B with a speed of S1 and back from Point B to Point A with a speed of S2, then

Avg, Speed = 2*S1*S2 / (S1 + S2)

Case 2  : If a body covers part of a journey at speed S1 and remaining part of the journey at speed S2 and the distance covered are in the ratio D1:D2, then

Avg. Speed = (D1 + D2)*S1*S2 / (D1*S2 + D2*S1 )

Had the distances been covered in ratios other than 1:1, then Case 1 would not give the right answer. We would have to use Case 2 then.

Please correct me if I'm wrong.

PareshGmat · Answer

Half the trip refers the distance

vards · Answer

Yes u r absolutely correct. I couldnt write the details of formula as comprehensively as u did. If equal distances are covered are covered at different speeds , then the formula for 2 speeds and 3 speeds applies as written in my post. If different distances are travelled , then the Case 2 in your post applies. +1 kudos to u :-D

Salvetor · Answer

https://wcrates.files.wordpress.com/2015/02/asfd.png

LaxAvenger · Answer

Hello,
could you kindly provide the steps of the equation to the solution s = 45 ?

ajdse22 · Answer

Two ways to solve this problem
equating time ... we know that the total time taken to travel x distance = x/60.. since 60 is the average speed. For simplicity we can take x= 60.
30/90+30/x = 1 => x = 45.

Another way that is even shorter. Let us get some distance that is a multiple of both 60 and 90. 180
90/90 + 90/x = 3=> 90/x = 2 => x =45.

Luckisnoexcuse · Answer

Assume the total length be 180 kms
Time taken when travelled at 60m/h will be 3 hrs

Time taken to travel half at 90 m/h was 1 hr

Time left 2 hrs , distance left 90 m

Speed will be 45m/h

Sent from my iPhone using GMAT Club Forum

A car travels from point A to point B. The average speed of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

A car travels from point A to point B. The average speed of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia